Let `'*'` be a binary operation on N given by `a*b=LdotCdotMdot(a , b)` for all `a , b in Ndot` Find `5*7,20*16` (ii) Is * commutative? Is * associative? Find the identity element in N Which element of N are invertible? Find them.

Explanation

Let *
be a binary operation on N given by `a`*`b=L.C.M.(a , b)`
for all `a , b in N`

i) `5`*`7= LCM of 5 and 7`

`=35` and

`20`*`16= LCM of 20 and 16=80`

ii) * is commutative, because `a`*`b= LCM of a and b= LCM of b and a=b`*`a`for all` a,b in N`

iii) * is also associative, because `a`*`(b`*`c)= LCM of a,b,c=(a`*b)`*`c` for `a,b,c in N`